# Capacitor Charge Time Calculator

Created by Luise Schwenke
Reviewed by Anna Szczepanek, PhD and Steven Wooding
Last updated: Jul 27, 2023

This is the capacitor charge time calculator — helping you to quickly and precisely calculate the charge time of your capacitor.

Here we answer your questions on how to calculate the charge time of a capacitor and how many time constants for a capacitor to fully charge does it take.

Type your values into the ready-to-use calculator or scroll down to get more comfortable with the topic through our comprehensive explanations and step-by-step example calculation.

## What is the capacitor charge time?

A capacitor stores electric charge in the form of an electrostatic field and will be charged or discharged during its use in the electric circuit. The charge time is the time it takes the capacitor to charge up to around 99%, reaching its charger's voltage (e.g., a battery).

Practically the capacitor can never be 100% charged as the flowing current gets smaller and smaller while reaching full charge, resulting in an exponential curve. This is why after a number of five multiples of the time constant, we regard the capacitor as fully charged. We'll explain the notion of time constant in the next section.

The capability of the capacitor to store energy is indicated in its capacitance. It is measured in farads (F). For a more detailed understanding of capacitance and parallel plate capacitors, our capacitance calculator is here to help you.

The resistor will affect our capacitor charge time, as it regulates the electric flow through the circuit. It is measured in ohms (Ω). With our Ohm's law resistance calculator, you can read precisely about calculating the resistance.

## How many time constants to charge a capacitor?

To calculate the charge time of a capacitor, we need to consider the time constant $\tau$ of the electric circuit, measured in seconds. It is the time it takes the capacitor to charge to 63.2% of its charger's voltage (e.g., a battery) through the resistor. It is also referred to as the delay time or transient response time, indicating the time response of the circuit when the input voltage is applied. It is calculated as follows:

$\tau = R \times C$

where:

• $\tau$ — Time constant (seconds);
• $R$ — Resistance (ohm); and
• $C$ — Capacitance (farads).

Using the time constant, we can write the relationship between the percentages of charge and the charge time $T$ as:

$\textrm{Percentage} = 1 - {\mathrm{e}^{-\frac T \tau}}$

It's common knowledge that after five time constants, the capacitor is regarded as fully charged, reaching a charge of around 99%. We can derive this information by applying the formulas above:

$1 - \mathrm{e}^{-\frac{5\tau}{\tau}} = 1 - \mathrm{e}^{-5} \approx 99.3\%$

## Formula for capacitor charge time

From the formula of the time constant above, we can now formulate the equation for the capacitor charge time as follows:

\begin{align*} T &= 5 \times τ\\ &= 5 \times R \times C \end{align*}

where:

• $T$ — Charge time (seconds);
• $\tau$ — Time constant (seconds);
• $R$ — Resistance (ohms); and
• $C$ — Capacitance (farads).

This formula gives you the time needed to fully charge the capacitor (i.e., up to around 99.3%).

As for charge time corresponding to other percentages of charge, we most often consider other multiples of time constant, i.e, the times of the form $T = \textrm{MTC} \times \tau$. The relationship reads:

$\textrm{Percentage} = 1 - {\mathrm{e}^{-\mathrm{MTC}}}$

Plugging in the consecutive natural numbers as $\mathrm{MTC}$, we obtain the following percentages of charge corresponding to the five first multiples of the time constant:

Time

Charged in percentage (%)

63.2

86.5

95.0

98.2

99.3

## Using the capacitor charge time calculator

Easily use our capacitor charge time calculator by taking the subsequent three steps:

1. First, enter the measured resistance in ohms or choose a subunit.

2. Second, enter the capacitance you measured in farads or choose a subunit.

3. Lastly, choose your desired percentage from the drop-down menu or the number of time constant τ to multiply with. You will see the other value adjusting automatically. The percentage is set to 99.3% charge by default, correlating to 5τ.

With the values inserted, you can now go ahead and calculate the charge time of your capacitor!

• You can also calculate the capacitance or resistance by entering two of the other values.

• If you need clarification on the SI units, our capacitor calculator will guide you through the capacitor code.

1. Hit the Advanced mode button at the bottom of our tool.

2. Enter your values for resistor and capacitance into the according fields.

3. Enter a specific percentage for the capacitor to charge up to. The correlating multiplicator for the time constant will adjust automatically.

4. Alternatively, you can enter the multiplicator for the time constant, that you want to calculate the charge time for. The correlating percentage will then adjust automatically.

5. See the calculator doing the magic for you, calculating the needed capacitor charge time!

## Example calculation for capacitor charge time

Imagine that we have an electric circuit with the following:

• A charged battery of 9 V;
• Capacitor with a capacitance of 1000 µF (= 0.001F); and
• Resistor of 3 KΩ (= 3000 Ω).

We want to know how to calculate the charge time of the capacitor.

Let's first calculate the time constant:

τ = R × C = 0.001 F × 3000 Ω = 3 s

The time constant is 3, which means that our capacitor takes 3 seconds to charge to 63.2%.

Now how many time constants to charge a capacitor do we need for 99.3% charge (full charge)?

To calculate the time of our capacitor to fully charged, we need to multiply the time constant by 5, so:

3 s × 5 = 15 s

Our example capacitor takes 15 seconds to charge fully.

You can also immediately insert the multiples of the time constant into the formula T = 5 × R × C:

T = 5 × 0.001 F × 3000 Ω = 15 s

The result is the same: It takes our capacitor 15 seconds to fully charge. Go give it a try in the capacitor charge-time calculator!

🔎 If you want a deeper dive into electric circuits, the RC circuit calculator will greatly help!

## Discharge time of a capacitor

As a capacitor can be charged, it can also be discharged by replacing the battery in the electric circuit.

The time for discharge follows analogous, where the time constant correlates to the charge percentage drop of about 37%. Similar to the charging, the discharging follows an exponential curve as the flowing current decreases over time. After five time constants, the capacitor is considered fully discharged, as the remaining charge is around 0.7%.

So, when questioning how many time constants for a capacitor to fully charge it takes, the answer applies to its discharge the same:

Time

Charged in percentage (%)

36.8

13.5

5.0

1.8

0.7

Luise Schwenke
Capacitor values
Resistance
Ω
Capacitance
μF
Time constant
sec
Charge time
Percentage
99.3%
Multiple of the time constant
5
time constant(s)
Charging Time
sec
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